Mx/G/1 retrial queue with multiple vacations and starting failures

This paper is concerned with the analysis of a single-server batch arrival re-trial queue with Bernoulli service schedule and multiple vacation with general retrial times and the server being subjected to starting failures. We assume that the customers who find the server busy are queued in the orbit in accordance with an FCFS (first-come-first-served) discipline and only the customer at the head of the queue is allowed access to the server. We first present the necessary and sufficient condition for the system to be stable and derive analytical results for the queue length distribution as well as some performance measures of the system under steady-state condition. We show that the general stochastic decomposition law for M^x/G/1 queue with multiple vacation models holds for the present system too. Some special cases are also studied.